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A New Variational Principle for a Nonlinear Dirac Equation on the Schwarzschild Metric

Paturel, Eric (2000), A New Variational Principle for a Nonlinear Dirac Equation on the Schwarzschild Metric, Communications in Mathematical Physics, 213, 2, p. 249-266. http://dx.doi.org/10.1007/s002200000243

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Type
Article accepté pour publication ou publié
Date
2000
Journal name
Communications in Mathematical Physics
Volume
213
Number
2
Publisher
Springer
Pages
249-266
Publication identifier
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Author(s)
Paturel, Eric
Abstract (EN)
In this paper, we prove the existence of infinitely many solutions of a stationary nonlinear Dirac equation on the Schwarzschild metric, outside a massive ball. These solutions are the critical points of a strongly indefinite functional. Thanks to a concavity property, we are able to construct a reduced functional, which is no longer strongly indefinite. We find critical points of this new functional using the Symmetric Mountain Pass Lemma. Note that, as A. Bachelot-Motet conjectured, these solutions vanish as the radius of the massive ball tends to the horizon radius of the metric.
Subjects / Keywords
nonlinear Dirac equation